Interference is difficult problem in wireless communications. For instance, the capacity region of two-user Gaussian interference channels has been an open problem for over thirty years. Recently, there has been some progress in understanding interference and extensive studies have been done regarding interference alignment (IA) techniques. Interference alignment (IA) was proposed in M. A. Maddah-Ali, A. S. Motahari, and A. K. Khandani, “Signaling over MIMO multi-base systems-combination of multi-access and broadcast schemes,” in Proc. of IEEE ISIT, Page(s) 2104-2108, 2006., and M. A. Maddah-Ali, A. S. Motahari, and A. K. Khandani, “Communication over MIMO X channels: Interference alignment, decomposition, and performance analysis,” IEEE Trans. on Information Theory, Vol. 54, no. 8, Page(s) 3457-3470, Aug. 2008, to reduce the effect of multi-user interference. IA was extended to deal with K pairs interference channels in Cadambe, V. R.; Jafar, S. A.; Shamai, S.; “Interference alignment and degrees of freedom of the K-user interference channel,” IEEE Trans. on Information Theory Vol. 54, No. 8, August 2008.
The key idea of IA is to reduce the dimension of the aggregated interference by aligning interference from different transmitters into a lower dimension subspace at each receiver. Using infinite dimension extension on the time dimension (time selective fading), it has been shown that the IA can achieve the optimal Degrees-of-Freedom (DoF) of
  KN  2in K-pair multiple input multiple output (MIMO) ergodic interference channels with N antennas at each node.
One important challenge of IA schemes is the feasibility condition. For instance, the IA schemes in Cadambe require O((KN)2K2N2) dimensions of signal space to achieve the
  KN  2total DoF. To avoid such huge dimensions of signal space, some researchers have studied IA designs for quasi-static (or constant) MIMO interference channels. With limited signal space dimensions, the achievable DoF of each transmitter-receiver pair in MIMO interference channels is upper bounded by
            N      t        +          N      r            K    +    1  (where K is the number of transmitter-receiver pairs, Nt, Nr are the number of antennas at each transmitter and receiver, respectively). Unlike the time-selective or frequency-selective MIMO interference channels, total DoF of quasi-static MIMO interference channels do not scale with K. Furthermore, it is challenging to design precoders and decorrelators (i.e beamforming vectors and zero-forcing vectors respectively) that satisfy the IA requirements in limited dimension MIMO interference channels due to feasibility problems.
In fact, the technical challenge on the feasibility issue in limited dimension MIMO interference channels is highly related to the full connectivity in the interference graph. However, in practice, the interference channels are usually partially connected due to path loss, shadowing as well as spatial correlation.
The above-described deficiencies of conventional IA techniques are merely intended to provide an overview of some of problems of current technology, and are not intended to be exhaustive. Other problems with the state of the art, and corresponding benefits of some of the various non-limiting embodiments described herein, may become further apparent upon review of the following detailed description.